Cuban spy René González, who was free on parole and had returned to Cuba to attend his father’s funeral, can remain on the island and will not have to return to finish his sentence in the United States if he agrees to renounce his U.S. citizenship, according to an order issued Friday by a federal judge in Miami.

The order unleashed a wave of speculation about whether it is linked to a possible exchange for Alan P. Gross, an American subcontractor for the U.S. Agency for International Development who has been jailed in Cuba since 2009, accused of distributing communication equipment to Jewish groups in Cuba.

González’s attorney told El Nuevo Herald, however, that U.S. District Judge Joan Lenard’s order authorizing his client to stay in Cuba had nothing to do with the Gross case.

“The judge’s order is limited only to my client,” attorney Phil Horowitz said.

Lenard’s decision closes a chapter in one of the most important Cuban espionage cases in the long, troubled history of tension between the United States and Cuba.

After a months-long trial in Miami in 2001, a federal jury found González, who was born in the United States to Cuban parents, and four other defendants — Gerardo Hernández, Antonio Guerrero, Ramón Labañino and Fernando González (no relation to René) — guilty of espionage.

All five were given different prison sentences. Hernández received two consecutive life sentences, while the rest, except René González, saw their original sentences reduced after appeal.

Hernández remains in prison serving two life sentences for conspiring to commit homicide because of his role in the downing of the Brothers to the Rescue’s planes by Cuban combat MiG planes in 1996, in which four people were killed: Carlos Costa, Armando Alejandre Jr., Mario de la Peña and Pablo Morales.

Labañino, Guerrero and Fernando González are serving sentences of 30, 22 and 18 years, respectively. René González was released from jail in October 2011 after serving 13 years, and he should have been on supervised parole for three more years.

González, interviewed in Cuba by The Associated Press, was pleased with the judge’s order, which responds to a legal petition he had submitted long ago.

“First, I have to read the order,” González told The Associated Press, emotionally. “I feel relieved. This was something I had requested.”

Maggie Alejandre Khuly, sister of Alejandre, one of the victims in the downed airplanes, expressed fear, not that the judge’s order could be the beginning of an exchange for Gross, but that it would lead to the exchange of Cuban spies for Joanne Chesimard, a fugitive American woman who arrived in Cuba after escaping from prison, where she had been sentenced for killing a New Jersey police officer in 1973.

“Our concern is that something may be beginning to happen. That this could be an initial signal of an exchange for this woman,” Alejandre Khuly said. “The fear is that Gerardo Hernández could be included in this.”

Hernández was the leader of the Avispa (Wasp) Network and he played a role in the shooting of the planes.

Alejandre Khuly said that an acceptable exchange would be for Cuba to hand over the two MIG pilots involved in the shooting of the planes, together with Gen. Rubén Martínez Fuentes, Cuba’s air force chief at the time.

U.S. officials have consistently denied any plans to exchange the spies for Gross. Even so, the judge’s decision upset some Cuban exiles.

“I respect our judicial system and I respect the judge’s decision,” said U.S. Rep. Ileana Ros-Lehtinen, R-Miami. “However, I disagree with it because the case of this convicted spy proves that you can inflict harm on your country of birth, spy in favor of an enemy state, serve only part of your sentence and, be released, even under restricted sentence … and then later retire to a quiet and prosperous life under the total protection of the Cuban regime.”

Ros-Lehtinen also said that it was unfair to grant González this privilege while Gross remained jailed in Cuba.

González is one of five Cuban intelligent agents sent to infiltrate military bases and Cuban exile groups. They created what is called the Wasp Network with about 15 members to carry out their mission. The Cuban government insists that they were only monitoring exiles and calls them “The Five Heroes.”

The FBI discovered the network and dismantled it in 1998, though not before it had infiltrated several exile groups, including Alpha 66, Comandos 4F, the Cuban American National Foundation and Brothers to the Rescue.

It was the infiltration of Brothers to the Rescue that shocked the exile community the most because the prosecutors were able to prove before a federal jury in a Miami court that members of the Wasp Network provided information to the Cuban intelligence that allowed it to target the planes that were shot down.

The network members also infiltrated a U.S. Navy base in Key West and attempted to infiltrate the Southern Command in Miami-Dade.